Consistent structures of invariant quadrature rules for the 𝑛-simplex

Maeztu, J. I.; Sáinz de la Maza, E.

doi:10.1090/S0025-5718-1995-1297473-8

Consistent structures of invariant quadrature rules for the $n$-simplex
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by J. I. Maeztu and E. Sáinz de la Maza PDF

Math. Comp. 64 (1995), 1171-1192 Request permission

Abstract:

In this paper we develop a technique to obtain, in a systematic way, the consistency conditions for the n-dimensional simplex ${T_n}$ for any dimension n and degree of precision d. The introduction of a convenient basis of invariant polynomials provides a powerful tool to analyze and obtain consistent structures. We also present tables listing the optimal consistent structures for dimensions $n = 2, \ldots ,8$ and degree of precision up to $d = 23$. This paper is devoted only to structures. No quadrature rules are presented here.

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